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Physics and Baseball: Having Your Cake and Eating it Too

Physics and Baseball: Having Your Cake and Eating it Too. Alan M. Nathan a-nathan@uiuc.edu webusers.npl.uiuc.edu/~a-nathan/pob Department of Physics University of Illinois. 1927 Yankees: Greatest baseball team ever assembled. 1927 Solvay Conference : Greatest physics team

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Physics and Baseball: Having Your Cake and Eating it Too

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  1. Physics and Baseball:Having Your Cake and Eating it Too Alan M. Nathan a-nathan@uiuc.edu webusers.npl.uiuc.edu/~a-nathan/pob Department of Physics University of Illinois

  2. 1927 Yankees: Greatest baseball team ever assembled 1927 Solvay Conference: Greatest physics team ever assembled MVP’s Baseball and Physics

  3. A great book to read…. “Our goal is not to reform the game but to understand it. “The physicist’s model of the game must fit the game.”

  4. A Physicist’s Approach to Current Issues in Baseball • Should aluminum bats be banned? • Corked bats and juiced balls—do they matter? • What the deal with the gyroball? • Can steroid use increase home run production? • Is the game different in Denver? • and what about that humidor?

  5. Some Experimental Tools • Bat testing facility • High-speed video or motion analysis “You can observe a lot by watching” ---Yogi • swinging the bat • ball-bat collision 1 • ball-bat collision 2 • PITCHf/x tracking system • Trackman radar more on these later See http://webusers.npl.uiuc.edu/~a-nathan/pob/video.html for some nifty videos.

  6. Some Physics Background • Physics of ball-bat collision • Aerodynamics of a baseball • Oblique collisions and spin

  7. Description of Ball-Bat Collision • forces large, time short • >8000 lbs, <1 ms • ball compresses, stops, expands • KEPEKE • bat recoils • lots of energy dissipated (“COR”) • distortion of ball • vibrations in bat • to hit home run…. • large batted ball speed • 100 mph~400 ft, each additional mph ~ 5-6’ • optimum take-off angle (300-350) • lots of backspin

  8. Kinematics of Ball-Bat Collision vball vbat BBS q=0.20 BBS = q vball + (1+q) vbat z • e:“coefficient of restitution” 0.50 • (energy dissipation—mainly in ball, some in bat) • r  mballz2/I6 :bat recoil factor = 0.25 • (momentum and angular momentum conservation) • ---heavier is better but…

  9. Batting cage study show how bat speed depends on I for college baseball players • ~ [1/I6]n 0<n<0.5 n  0.3 aluminum wood

  10. Accounting for COR: Dynamic Model for Ball-Bat Collision AMN,Am. J. Phys, 68, 979 (2000) • Collision excites bending vibrations in bat • hurts! breaks bats • dissipates energy • lower COR, BBS • Dynamic model of collision • Treat bat as nonuniform beam • Treat ball as damped spring

  11. f1 = 179 Hz f3 = 1181 Hz f2 = 582 Hz f4 = 1830 Hz frequency time Modal Analysis of a Baseball Bat www.kettering.edu/~drussell/bats.html

  12. Vibrations, COR, and the “Sweet Spot” Strike bat here + best performance & feel @ ~ node 2 e vf Evib

  13. Independence of End Conditions • strike bat in barrel—look at response in handle • handle moves only after ~0.6 ms delay • collision nearly over by then • nothing on knob end matters • size, shape • boundary conditions • hands! • confirmed experimentally

  14. Why Is Aluminum Better Than Wood? Aluminum has thin shell • Less mass in barrel • --lower MOI, higher bat speed, easier to control  • --but lower collision efficiency  • --partially canceling effects • “Hoop modes” • trampoline effect  • “ping” (~2000 Hz) demo

  15. The “Trampoline” Effect: A Simple Physical Picture • Two springs mutually compress each other • KE  PE  KE • PE shared between “ball spring” and “bat spring” • …sharing depends on “kball/kbat” • PE in ball mostly dissipated(~80%!) • PE in bat mostly restored • Net effect: less overall energy dissipated • ...and therefore higher ball-bat COR • …more “bounce”—confirmed by experiment • …and higher BBS • Also seen in golf, tennis, … demo

  16. Regulating Performance of Non-Wood Bats:A Science-Based Approach Used by NCAA BBS = q vball + (1+q) vbat • Specify maximum q • approx. same as for wood bats of similar wt. • implies bats swung alike will perform alike • Specify minimum MOI to limit bat speed • smaller than wood • Together, these determine a maximum BBS • gap between wood and aluminum  5% • does that mean aluminum should be banned? • an issue many are struggling with

  17. What About Corked Bats?or..What was Sammy thinking? no trampoline effect! • Conclusion: • No increase in BBS • increase in swing speed • decrease in collision efficiency • ~ [1/I6]n 0<n<0.5

  18. What About Juiced Baseballs? Conclusion: No evidence for juiced ball

  19. FM  Fd Fd=½ CDAv2 mg FM= ½ CMARv Courtesy, Popular Mechanics direction leading edge is turning Aerodynamics of a Baseball • Gravity • Drag (“air resistance”) • Lift (or “Magnus”)

  20. “Drag crisis?” Typical values of drag and lift

  21. Effect of Drag and Lift on Trajectories FM  Fd mg • drag effect is huge • lift effect is smaller but significant

  22. Some Effects of Drag • Reduced distance on fly ball • Reduction of pitched ball speed by ~10% • Asymmetric trajectory: • Total Distance  1.7 x distance at apex • Optimum home run angle ~30o-35o

  23. FM  Fd mg Some Effects of Magnus • Backspin makes ball rise • “hop” of fastball • undercut balls: increased distance, reduced optimum angle of home run • Topspin makes ball drop • “12-6” curveball • topped balls nose-dive • Breaking pitches due to spin • Cutters, sliders, etc.

  24. The PITCHf/x Tracking SystemA Quantitative Tool to Study Pitched Baseball Trajectories

  25. How Does PITCHf/x Work? • Two video cameras track baseball in 1/60-sec intervals • usually “high home” and “high first” • third CF camera used establishes ht. of strike zone • Pattern-recognition software to identify “blobs” • Camera calibration to convert pixels to (x,y,z) • 9-parameter fit to trajectory • constant acceleration for x(t),y(t),z(t) • Use fit to calculate lots of stuff • The full trajectory • The “break” • Drag and Magnus forces

  26. Example: Drag and Drag Coefficients20k pitches from Anaheim, 2007

  27. Using PITCHf/x to Classify PitchesJon Lester, Aug 3, 2007 @ Seattle spin axis LHP Catcher’s View I: Nearly overhand fastball II: Slider or cut fastball III: ¾ Fastball IV: Curveball break direction = -90o

  28. Courtesy, Ryutaro Himeno Daisuke Matsuzaka: Does he or doesn’t he? What’s the Deal with the Gyroball?

  29. From PITCHf/x to HITf/xBarry Bond’s 756th Home Run • PITCHf/x data tracked hit ball over first 20 ft • Precision measurement of endpoint and time-of-flight • Inferred: v0=112 mph; =27o up; =16o to right of dead center; =1186 rpm (backspin) and 189 rpm (sidespin, breaking to center)

  30. Baseball Aerodynamics:Things I would like to know better • Better data on drag • “drag crisis”? • spin-dependent drag? • drag for v>100 mph • Dependence of drag & Magnus on seam orientation, surface roughness, … • Is the spin constant?

  31. Trackman: The Wave of the Futuresee www.trackmangolf.com • Doppler radar to measure radial velocity • 3-detector array to measure phase • two angles • Sidebands gives spin magnitude • Result: • in principle, full trajectory can be reconstructed, including spin and spin axis • already in use for golf, currently being adapted for baseball

  32. thanks to Fredrik Tuxen, CTO of Trackman

  33. Oblique Collisions:Leaving the No-Spin Zone Oblique  friction  spin still need a good collision model my model: slide, then roll Familiar Results: Balls hit to left/right break toward foul line Topspin gives tricky bounces in infield Backspin keeps fly ball in air longer Tricky popups to infield

  34. Ball100 downward D = center-to-center offset Bat 100 upward What’s going on here?? Undercutting the ball  backspin trajectories “vertical sweet spot”

  35. Another familiar result: bat hits under ball: popup to opposite field bat tilted downward Catcher’s View bat hits over ball: grounder to pull field

  36. Steroids and Home Run Productonsee Roger Tobin, AJP, Jan. 2008 • Steroids increases muscle mass • Increased muscle mass increases swing speed • Increased swing speed increase BBS • Increased BBS means longer fly balls • Longer fly balls means more home runs

  37. Home Run Distances, 2007 www.hittrackeronline.com Delta = distance beyond fence (ft) ~4% per foot Tobin’s Conclusion: increase of BBS by few mph can increase HR rate by 30-50%!

  38. Steroids and Bat Speed • Batter supplies energy proportional to M • Energy shared between bat and some fraction 2of M • Roughly: 2 ~ 0.01 • So roughly, 10% increase in M gives • ~2.5% increase in vbat • ~2 mph increase in BBS • ~12 additional ft. on long fly ball • ~20% (Adair) -50% (Tobin) more home runs!

  39. Work in Progress • Collision experiments & calculations to elucidate trampoline effect • New studies of aerodynamics using Trackman and PITCHf/x • Experiments on high-speed oblique collisions—does slide-then-roll model work? • A book, with Aussi Rod Cross

  40. 2004 2007 Final Summary • Physics of baseball is a fun application of basic (and not-so-basic) physics • Check out my web site if you want to know more • webusers.npl.uiuc.edu/~a-nathan/pob • a-nathan@uiuc.edu • Thanks for your attention and go Red Sox!

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